armaGARCH

INTRADAY

Timeline: 2019-08-29 09:35:00 - 2020-11-20 16:10:00

# g <- ggplot(data=intra) + theme_classic() +
#   geom_line(aes(x=Date,y=SPX)) +
#   scale_y_continuous(limits=c(0, 50)) +
#   labs(x="Date", y="S&P 500 Price")


ay <- list(
  tickfont = list(color = "red"),
  overlaying = "y",
  side = "right",
  title = "S&P 500 Volatility"
)

fig <- plot_ly() 
fig <- fig %>% add_lines(x = intra$Date, y = intra$SPX, name = "S&P 500 Price")
fig <- fig %>% add_lines(x = intra$Date, y = intra$e, name = "S&P 500 Volatility", yaxis = "y2",opacity = 0.5)
fig <- fig %>% add_lines(x = as_datetime("2020-03-03 10:00:00   "), y = intra$e, name = "Rate Cut 03/03", yaxis = "y2",opacity = 1.0)
fig <- fig %>% add_lines(x = as_datetime("2020-03-16 09:45:00   "), y = intra$e, name = "QE 03/15", yaxis = "y2",opacity = 1.0)
fig <- fig %>% add_lines(x = as_datetime("2020-03-23 09:30:00   "), y = intra$e, name = "QE 03/23", yaxis = "y2",opacity = 1.0)
fig <- fig %>% add_lines(x = as_datetime("2020-04-06 09:30:00   "), y = intra$e, name = "LF 04/06", yaxis = "y2",opacity = 1.0)
fig <- fig %>% add_lines(x = as_datetime("2020-04-28 09:30:00   "), y = intra$e, name = "LF 04/27", yaxis = "y2",opacity = 1.0)
fig <- fig %>% add_lines(x = as_datetime("2020-07-28 09:30:00   "), y = intra$e, name = "LF 07/28", yaxis = "y2",opacity = 1.0)


fig <- fig %>% layout(
    title = "S&P 500 Index Level and Return Volatility", yaxis2 = ay, 
    xaxis = list(title="Date"), yaxis1 = list(title = "S&P 500 Index")
  )
fig

# htmlwidgets::saveWidget(fig, "fig.html", selfcontained = F, libdir = "lib")

# g + geom_line(data = intra, aes(x=Date,y=e))  +
#   scale_y_continuous(limits=c(-0.1, 0.1),
#                      sec.axis = sec_axis(~ . *0.1, name = "name of the new axis"))

fed <- read_csv("fredgraph/Weekly_As_of_Wednesday.csv", col_types = cols(DATE = col_character()))
all <- read_csv("fredgraph/Weekly_Ending_Wednesday.csv", col_types = cols(DATE = col_character())) %>%
  full_join(fed, by = "DATE")%>% na.omit()

by <- list(
  tickfont = list(color = "red"),
  overlaying = "y",
  side = "right"
)

figQE <- plot_ly() 
figQE <- figQE %>% add_lines(x = as.Date(all$DATE), y = all$WALCL, name = "Assets: Total Assets (Less Eliminations from Consolidation): Wednesday Level (in mm)")
figQE <- figQE %>% add_lines(x = as.Date(all$DATE), y = all$SP500, name = "S&P 500: Week ending Wednesday",yaxis = "y2",opacity = 0.5)

figQE <- figQE %>% layout(
    title = "The US Fed's Total Assets (Less Eliminations from Consolidation)", yaxis2 = by, 
    xaxis = list(title="Date")
  )

figQE

GARCH

EGARCH (1,1)

events_intra <- read_csv("data/event_lists/events_intra.csv", 
    col_types = cols(Date = col_datetime(format = "%m/%d/%y %H:%M")))
# events----
hr1_315 <- ts(events_intra[,2])
hr2_315 <- ts(events_intra[,3])
hr3_315 <- ts(events_intra[,4])
hr4_315 <- ts(events_intra[,5])
hr5_315 <- ts(events_intra[,6])
hr6_315 <- ts(events_intra[,7])

hr1_33 <- ts(events_intra[,8])
hr2_33 <- ts(events_intra[,9])
hr3_33 <- ts(events_intra[,10])
hr4_33 <- ts(events_intra[,11])
hr5_33 <- ts(events_intra[,12])
hr6_33 <- ts(events_intra[,13])

hr1_323 <- ts(events_intra[,14])
hr2_323 <- ts(events_intra[,15])
hr3_323 <- ts(events_intra[,16])
hr4_323 <- ts(events_intra[,17])
hr5_323 <- ts(events_intra[,18])
hr6_323 <- ts(events_intra[,19])

hr1_46 <- ts(events_intra[,20])
hr2_46 <- ts(events_intra[,21])
hr3_46 <- ts(events_intra[,22])
hr4_46 <- ts(events_intra[,23])
hr5_46 <- ts(events_intra[,24])
hr6_46 <- ts(events_intra[,25])

hr1_427 <- ts(events_intra[,26])
hr2_427 <- ts(events_intra[,27])
hr3_427 <- ts(events_intra[,28])
hr4_427 <- ts(events_intra[,29])
hr5_427 <- ts(events_intra[,30])
hr6_427 <- ts(events_intra[,31])

hr1_625 <- ts(events_intra[,32])
hr2_625 <- ts(events_intra[,33])
hr3_625 <- ts(events_intra[,34])
hr4_625 <- ts(events_intra[,35])
hr5_625 <- ts(events_intra[,36])
hr6_625 <- ts(events_intra[,37])

hr1_728 <- ts(events_intra[,38])
hr2_728 <- ts(events_intra[,39])
hr3_728 <- ts(events_intra[,40])
hr4_728 <- ts(events_intra[,41])
hr5_728 <- ts(events_intra[,42])
hr6_728 <- ts(events_intra[,43])

# events + external----
ext_reg_intra   <- cbind(v1, d1, hr1_315,hr2_315,hr3_315,hr4_315,hr5_315,hr6_315,
                         hr1_33, hr2_33, hr3_33, hr4_33, hr5_33, hr6_33,
                         hr1_323, hr2_323, hr3_323, hr4_323, hr5_323, hr6_323,
                         hr1_46, hr2_46, hr3_46, hr4_46, hr5_46, hr6_46, 
                         hr1_427, hr2_427, hr3_427, hr4_427, hr5_427, hr6_427,
                         hr1_625, hr2_625, hr3_625, hr4_625, hr5_625, hr6_625,
                         hr1_728, hr2_728, hr3_728, hr4_728, hr5_728, hr6_728) %>% na.omit()

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : eGARCH(1,1)
## Mean Model   : ARFIMA(1,0,0)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error     t value Pr(>|t|)
## mu     -0.000003    0.000001 -6.2509e+00 0.000000
## ar1    -0.020700    0.004175 -4.9582e+00 0.000001
## mxreg1 -0.088507    0.000521 -1.6995e+02 0.000000
## mxreg2 -0.096713    0.008093 -1.1949e+01 0.000000
## omega  -0.011660    0.000378 -3.0834e+01 0.000000
## alpha1 -0.010086    0.001822 -5.5344e+00 0.000000
## beta1   0.999303    0.000006  1.6674e+05 0.000000
## gamma1  0.067807    0.003922  1.7288e+01 0.000000
## vxreg1  0.103850    0.097261  1.0678e+00 0.285631
## vxreg2  0.006374    0.103451  6.1613e-02 0.950871
## vxreg3 -0.111524    0.103348 -1.0791e+00 0.280536
## vxreg4  0.070189    0.106450  6.5936e-01 0.509665
## vxreg5  0.013640    0.094947  1.4366e-01 0.885771
## vxreg6  0.099399    0.063392  1.5680e+00 0.116880
## shape   2.372799    0.043506  5.4539e+01 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu     -0.000003    0.000001 -3.0741e+00 0.002111
## ar1    -0.020700    0.005422 -3.8176e+00 0.000135
## mxreg1 -0.088507    0.001825 -4.8500e+01 0.000000
## mxreg2 -0.096713    0.021931 -4.4098e+00 0.000010
## omega  -0.011660    0.000691 -1.6883e+01 0.000000
## alpha1 -0.010086    0.004072 -2.4765e+00 0.013266
## beta1   0.999303    0.000008  1.2064e+05 0.000000
## gamma1  0.067807    0.008227  8.2419e+00 0.000000
## vxreg1  0.103850    0.054700  1.8985e+00 0.057626
## vxreg2  0.006374    0.053825  1.1842e-01 0.905735
## vxreg3 -0.111524    0.043099 -2.5876e+00 0.009664
## vxreg4  0.070189    0.053908  1.3020e+00 0.192916
## vxreg5  0.013640    0.048644  2.8040e-01 0.779168
## vxreg6  0.099399    0.035018  2.8385e+00 0.004533
## shape   2.372799    0.074891  3.1683e+01 0.000000
## 
## LogLikelihood : 154225.8 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -12.208
## Bayes        -12.204
## Shibata      -12.208
## Hannan-Quinn -12.207
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                   0.005614  0.9403
## Lag[2*(p+q)+(p+q)-1][2]  0.230046  0.9979
## Lag[4*(p+q)+(p+q)-1][5]  2.669852  0.5187
## d.o.f=1
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.03938  0.8427
## Lag[2*(p+q)+(p+q)-1][5]   0.06815  0.9991
## Lag[4*(p+q)+(p+q)-1][9]   0.18074  1.0000
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]  0.009851 0.500 2.000  0.9209
## ARCH Lag[5]  0.014347 1.440 1.667  0.9992
## ARCH Lag[7]  0.102014 2.315 1.543  0.9993
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  140.8292
## Individual Statistics:                
## mu     1.028e+00
## ar1    2.314e+00
## mxreg1 1.063e+02
## mxreg2 2.265e+01
## omega  3.569e+00
## alpha1 6.079e-01
## beta1  3.681e+00
## gamma1 1.167e+00
## vxreg1 2.891e-04
## vxreg2 3.940e-04
## vxreg3 5.170e-04
## vxreg4 7.799e-04
## vxreg5 9.904e-04
## vxreg6 1.427e-03
## shape  4.849e+00
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          3.26 3.54 4.07
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           0.6298 0.5288    
## Negative Sign Bias  0.5764 0.5643    
## Positive Sign Bias  0.9187 0.3582    
## Joint Effect        1.5084 0.6803    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     101.4    2.931e-13
## 2    30     126.8    3.437e-14
## 3    40     165.8    1.445e-17
## 4    50     165.6    1.454e-14
## 
## 
## Elapsed time : 43.53416

OTHER EVENTS

hour_impact_all <-hour_impact_all%>% 
  filter(!str_detect(event, "625"))
  
lcols = c("black","darkred","steelblue","orange","purple","red")
linetype = c(rep(c('solid', 'dashed', 'dotted'),2))
llegend = c("March 15 - QE", "March 23 - QE", "March 3 - Rate Cut", "April 27 - Credit Facility",
            "April 6 - Credit Facility", "July 28 - Credit Facility")
tlegend = "Event"

hour_all <- ggplot(data =hour_impact_all, aes(x=h, y=percent_change)) +
  geom_line(aes(color = event, linetype = event)) +
  scale_color_manual(values = lcols, labels = llegend, name = tlegend) +
  scale_linetype_manual(name = tlegend, labels = llegend,values = linetype) +
  theme_minimal() + theme(panel.grid.minor = element_blank(),
                          panel.grid.major = element_line(color="#66CCFF", 
                                                          size=0.1, linetype="dashed"),
                          axis.line.x.bottom = element_line(),
                          axis.line.y = element_line(),
                          text = element_text(family="Palatino"),
                          legend.position = "right",
                          legend.title = element_text(size = 12),
                          legend.text = element_text( size = 10),
                          plot.title = element_text(face = "bold", hjust = 0.5)) +
  labs(x="Hours from event", y="Volatility Change (%)", 
       title="Hourly change in S&P volatility after major FOMC announcements") +
  scale_x_continuous(breaks=c(0,1,2,3,4,5,6)) #+
  # scale_y_continuous(labels = scales::percent)

hour_all

ggsave("final-fig/sixhour.png", hour_all, height = 5.2, width = 9.6, dpi = 600)

lcols = c("black","darkred","darkcyan","orange")
linetype = c(rep(c('solid', 'dashed'),2))
llegend = c("March 15 - QE", "March 23 - QE",
            "April 6 - Credit Facility", 
            "July 28 - Credit Facility")
tlegend = "Event"

hour_impact_some <- hour_impact_all%>% 
  filter(!str_detect(event, "33")) %>% filter(!str_detect(event, "427")) # %>% filter(!str_detect(event, "625"))

hour_some <- ggplot(data =hour_impact_some, aes(x=h, y=percent_change)) +
  geom_line(aes(color = event, linetype = event)) +
  scale_color_manual(values = lcols, labels = llegend, name = tlegend) +
  scale_linetype_manual(name = tlegend, labels = llegend,values = linetype) +
  theme_minimal() + theme(panel.grid.minor = element_blank(),
                          panel.grid.major = element_line(color="#66CCFF", 
                                                          size=0.1, linetype="dashed"),
                          axis.line.x.bottom = element_line(),
                          axis.line.y = element_line(),
                          text = element_text(family="Palatino"),
                          legend.position = "bottom",
                          legend.title = element_text(size = 12),
                          legend.text = element_text( size = 10),
                          plot.title = element_text(face = "bold", hjust = 0.5)) +
  labs(x="Hours from event", y="Volatility Change (%)", 
       title="Hourly change in S&P volatility after major FOMC announcements",
       caption = "Note: Events on March 3, April 27, and June 25 could be found in the Appendix") +
  scale_x_continuous(breaks=c(0,1,2,3,4,5,6)) 
  # scale_y_continuous(labels = scales::percent) 

hour_some

ggsave("final-fig/some-sixhour.png", hour_some, height = 5.2, width = 9.6, dpi = 600)